He was the founder of Borchs Kollegium and is noted for being the influential instructor of scientist Nicolas Steno.

In 1655, Borch was summoned to raise the sons of Gersdorff, a position he held for five years.

He visited his former pupil Nicolas Steno, Johann Glauber, Giuseppe Francesco Borri and Comenius.

His well recorded journals of his travels are an important document of the European scientific climate in the 17th century.

Borch is commemorated in the scientific name of a species of South American snake, Siagonodon borrichianus.